Commercial communication systems today strive for the highest possible spectral and power efficiency at the lowest possible cost, complexity and overall energy consumption. In order to reach the high spectral efficiencies required to support the necessary data rates in networks today, phase-coherent signaling are often used, especially in microwave backhaul systems which operate at a high signal to noise ratio, SNR.
As an example, consider the single carrier system 100 for phase-coherent signaling shown in FIG. 1. The system 100 is a transmitter-receiver chain, where the transmitter 20 receives a baseband signal, BB, which is modulated in a modulator 10, filtered in a low pass filter 11, and then “up-converted” to radio frequency, RF, in a transmitter unit Tx 12 by means of a transmit oscillator, before being transmitted by means of a transmitter antenna 21. The receiver 23 receives the transmitted signal via a receiver antenna 22, “down-converts” it to a lower frequency by means of a receiver oscillator comprised in a receive unit Rx 13, filtered in a low-pass filter 14, passed through a carrier recovery unit 15, which is connected to a detector 16, and finally demodulated in a demodulator 17, so that the BB signal which was input to the transmitter unit 20 is recovered on the receiver side.
The systems 100 performance in terms of data throughput and bit error rate, BER, is in practice limited by non-ideal physical components in both the transmitter and in the receiver. Examples of degrading factors introduced by non-ideal components include additive noise, introduced mainly by electrical components in the receiver 22, and phase noise introduced mainly by imperfections in the oscillators which are included in the transmit unit Tx 12 and in the receive unit Rx 13.
Regarding the terms “additive noise” and “phase noise” which have been used above, these terms are here used in the sense that additive noise is noise that adds to the amplitude and phase of the signal, while phase noise is noise that adds to the phase of the signal. Phase noise and additive noise are accumulated throughout the communication system, and are quantified at the output of the receive unit Rx 205.
The additive noise in the system 100 is suppressed to some extent by means of passive matched filtering at the transmitting and the receiving ends of the system. The phase noise, on the other hand, is compensated for actively by some type of phase tracking system or carrier recovery unit, where well-known methods for carrier recovery include Phase Locked Loop (PLL) based approaches and Kalman filtering.
The modulator 10 and the demodulator 17 of FIG. 1 may be a “mapper” and a corresponding “demapper” for a 1024-QAM constellation, as an alternative to which the information carried in the phase of the signal could be differentially encoded and then demodulated. Compared to a directly modulated QAM-signal that carries information in amplitude and instantaneous phase, a differentially encoded signal carries information directly in amplitude but in the difference in phase between consecutive symbols. In such systems, the accumulated random fluctuations in phase caused by non-ideal oscillators do not need to be tracked over time, since the cumulative phase noise process is absorbed by the differential encoding of the signal.
Significant efforts have been spent in trying to improve algorithms and methods for carrier recovery, the reason being that the better the carrier recovery algorithm performs, the less expensive and power consuming oscillators can be used in the system. These efforts have resulted in algorithms with high performance, but also with high complexity as compared to the low complexity classic methods based on, e.g., PLLs. Hence, the performance problem associated with “legacy” carrier recovery methods has been alleviated, while introducing complexity issues.
A drawback of many advanced systems for carrier recovery based on, e.g., the expectation maximization (EM) method or factor graph methods is that they rely on stochastic models of the system. If such models are not correct, then the stability of the entire communication system is at risk.
Another drawback associated with most carrier recovery methods is that they compute (often iteratively) a phase estimate based on an error signal that is derived from detecting the transmitted data. Hence, they require knowledge of, e.g., the modulation format and rate that is used for communication. Also, detection errors will affect the quality of the error signal, and may lead to an error prone system or to system instability.
A differentially encoded and demodulated communication system is, as noted above, much less sensitive to phase fluctuation. However, in a typical differentially demodulating receiver, it can be shown that a signal to noise ratio, SNR, penalty of 3 dB is incurred in the phase channel.